TIME SERIES APPROACHES TO TESTING INCOME
CONVERGENCE IN MENA COUNTRIES
HALUK ERLAT
Department of Economics
Middle East Technical University
06531 Ankara, Turkey
Fax: 90-312-2107964
Email: herlat@metu.edu.tr
Prepared for presentation at the 27th Annual Meeting of the Middle East
Economic Association, January 5-7, 2007, Chicago, USA.
.
1. Introduction
Our objective is to test for income convergence in the Middle East and North African
(MENA) countries using time series techniques. Income convergence for these countries was
tested, previously and quite extensively, by Guetat and Serranito (2004), using panel root
tests. Underlying this approach is the assumption that the per capita income of countries
approach or diverge from a target level which may either be the average of the per capita
income of the group of countries being considered (which is what Guetat and Serranito use) or
the per capita income of an advanced country. Pesaran (2006), however, argues that the
choice of such a target level may be arbitrary and that, following Bernard and Durlauf (1995),
the pair-wise convergence of all countries involved should be investigated.
Pesaran (2006) shows that, to overcome the dimensional limitations of the
cointegration approach used by Bernard and Durlauf (1995), the stationarity of the pair-wise
logarithmic differences between the per capita incomes may be tested. If N is the number of
countries, then one has to carry out N ( N  1) / 2 unit root tests, which may be quite a large
number if N is large, even moderately so. In fact, Pesaran (2006) has applied his approach to
the per capita incomes of various groups of countries (including the MENA countries), the
largest of which consisted of 101 series and this implied that 5050 unit root tests were
performed. Of course, the number of countries to be considered in our case, as we shall
explain below, is only nine which implies 36 pairs of countries but we, nevertheless, decided
to use a screening procedure due to Webber and White (2004) where, roughly speaking, for a
given period, the per capita income difference between two countries at the end of the period
is compared, in ratio terms, to the income difference at the beginning of the period and
countries are said to be converging if this ratio lies between zero and unity. Pesaran’s
procedure was applied to those countries that satisfied this requirement.
The plan of our paper will, then, be as follows. In the following section, an account of
the empirical methods will be given. In Section 3 the data will be described and the empirical
results will be presented in Section 4. The final section will contain our conclusions.
2. Methodology
We shall investigate convergence in two stages. We shall first use a descriptive
method due to Webber and White (2004), by which we shall reduce the number of pair wise
tests of convergence that we shall conduct. We shall then perform pair-wise unit root tests.
1
Let y it and y jt denote the per capita incomes of countries i and j at time t respectively.
The descriptive method is based on investigating the behaviour of y it vis-à-vis y jt by looking
at their differences in two points in time, namely, y it  y jt versus y i ,t  h  y j .t  h . If
y it  y jt  y i ,t  h  y j .t  h then one may take this as evidence of convergence since it implies
that country i grows slower than country j. Similarly, one may compare y it y jt with
y i ,t  k y j ,t  k or ln y it  ln y jt with ln y i ,t  h  ln y j .t  h , which is the same thing. We may then
state that

If the observations converge in both ratios and differences, we have strong
convergence

If the observations converge in ratios or differences, we have weak convergence.
It is also possible that y it  y jt but y i ,t  h  y j .t  h , i.e., the countries may switch positions.
The procedure described below takes switching also account.
We shall assume, throughout, that y it  y jt . Hence, for convergence in ratio we shall
calculate
X i, j 
(1)
ln y i ,t  k  ln y j ,t  k
ln y it  ln y jt
and conclude that if,

X ij  1 , countries i and j diverge in ratio without switching.

0  X ij  1 , countries i and j converge in ratio without switching.

 1  X ij  0 , countries i and j converge in ratio with switching.

X ij   1 , countries i and j diverge in ratio with switching.
For convergence in difference, we first apply a normalizing transformation on y it as
(2)
cit 
yit  yt
yt
2
where yt  i 1 yit / N , so that any bias that may result from ignoring the growth of the N
N
countries as a group is avoided. We then calculate
Yij 
(3)
c i ,t  k  c j ,t  k
cit  c jt
and conclude that if

Yij  1 , countries i and j diverge in ratio without switching.

0  Yij  1 , countries i and j converge in ratio without switching.

 1  Yij  0 , countries i and j converge in ratio with switching.

Yij   1 , countries i and j diverge in ratio with switching.
Thus,

0  X ij  1 and 0  Yij  1 would imply strong convergence without switching.

0  X ij  1 or 0  Yij  1 would imply weak convergence without switching.

 1  X ij  0 and  1  Yij  0 would imply strong convergence with switching.

 1  X ij  0 or  1  Yij  0 would imply weak convergence with switching.
After having classified the pairs of countries, we shall choose those that exhibit strong
convergence with or without switching and apply pair wise tests of convergence. The
investigation of convergence using a pair wise approach is based on the definition of
convergence for two countries provided by Bernard and Durlauf (1995):
(4)
lim k  E ( wi ,t  k  w j ,t  k | I t )  0 at any fixed time t
where wit  ln yit and I t is the information set at time t, containing the current and past
values for wi ,t  k for i  1,..., N and k  0, 1, 2,  , . From this definition, it is concluded that in
order for countries i and j to converge, their per capita outputs should be cointegrated with
cointegrating vector (1,-1).
Pesaran (2006) offers an alternative definition based on the probability of the output
gap wit  w jt falling outside a predetermined interval; i.e., that the probability of
3
| wi ,t  k  w j ,t  k | being larger than some finite positive constant g should be smaller than some
preassigned small probability,  , for all horizons, k. Using this definition avoids the pretesting for unit roots in wit and w jt that the cointegration approach, advocated by Bernard and
Durlauf (1995), requires. wit  w jt may now be tested, first, for the presence of a unit root in
an autoregression that contains a linear trend and, if no unit root is found, for the presence of a
linear deterministic trend.
When there are more than two countries to consider, Pesaran (2006) offers a definition
which, basically, requires that the definition of convergence given for a pair of countries
should hold for all N(N-1)/2 pairs of countries being considered. Hence, unit root tests are
applied to all the pairs chosen in the first stage of our investigation and to conclude that there
is convergence in the group, all pairs must converge..
We initially followed Pesaran (2006) and implemented the ADF test, where the null
hypothesis is divergence, and the KPSS (Kwiatowski et al, 1992) test where the null
hypothesis is convergence. Let z it  wit  w jt . Then the ADF test was obtained by estimating
P
 z ijt  d tr  r  z ijt    i z ijt   ijt , r  0,1
(5)
i 1
where d tr  1 and  r   0 for r = 0 and d tr  (1, t ) and  r  (  0 , 1 ) for r = 1, and the tratio of  was used as the statistic to test for a unit root. In the case of r =1, 1  0 was
tested for those cases where the null hypothesis of   0 were rejected.
The KPSS test, on the other hand, is based on assuming that the z ijt are stationary so
that they are generated by
(6)
z ijt   0   ijt
Under the alternative hypothesis of nonstationarity, it is assumed that  0t   0  ut , i.e., a
random walk, with E (ut )  0 and E(ut )   u2  0 . Hence, the null hypothesis of stationarity
2
becomes H o :  u2  0 vs H 1 :  u2  0 . The test statistic for this hypothesis is based on the
Lagrange Multiplier approach and is obtained as
4
T
(7)
where
KPSSij 
T  2  S ijt
t

S ijt   1  ij ,
t 1
ˆ 2


 

ˆ   T 1 t 1  ijt2  2T 1 1 w(m l ) t 1  ijt ij,t l ,
T
m
T

w(m l )  1  ( /( m  1)) and the  ijt are obtained from the OLS estimation of (6). The choice
of m was made using a data dependent procedure due the Newey and West (1994).
The results of our descriptive approach and the plots of the pair-wise differences led to
the expectation that structural shifts in the level of the output gaps, i.e., the intercept term in
(5), needed to be taken into account when testing for unit roots. We did this by following the
approach developed by Perron and Vogelsang (1992) and Perron (1997) where the shift in  0
is taken to be endogeneous. Such tests are sequential tests. For the single shift case that we
shall consider, we start at a shift point t  h0 , where h0  [T ] and  is an appropriately
chosen trimming fraction, and estimate (5) sequentially as this shift point is moved towards
t  T  h0 . This may be done by using the dummy variables
(8)
DU t (h)  0
1
Dt (h)  1
for t  1,, h
for t  h  1,, T
for t  1,, h
 0 otherwise
where h0  h  T  h0 . We would then be estimating
p
(9)
zijt  d tr   DU t (h)  Dt (h)  yt 1    s zij,t s   ijt
s 1
The test statistics is simply the minimum value of the sequentially obtained ADF statistics

(min ADF) and the shift point, h will be the date corresponding to this minimized value.1
1
Perron and Vogelsang (1992) and Perron (1997) call this the innovational outlier model, implying that the shift
in the intercept term is gradual.
5
3. The Data
The data were obtained from the Penn World Tables Version 6.1 (Heston, Summers
and Aken, 2002). They consist of annual Purchasing Power adjusted per capita real GDP
series constructed in international dollars at 1996 prices. Even though the series are
constructed to cover the 1951-2000 period only four MENA countries have data for this
period; Israel, Egypt, Morocco and Turkey. We, thus, used the 1961-2000 period for which
data exist for nine countries; Algeria, Egypt, Iran, Israel, Jordan, Morocco, Syria, Tunisia and
Turkey. The same data have also been utilized by Guitat and Serranito (2004) and Pesaran
(2006).
4. Empirical Results
We first consider the results of the descriptive procedure used in the first stage. We
considered four base years, 1961, 1970, 1980 and 1990. We then calculated the X ij and Yij
values using equations (1) and (3). The results are given in Table 1 and in Tables A1-A3 in
the Appendix.
To see how we may use these results, let us consider the 1961-based figures for
Algeria as presented in Table 1. We find that Algeria strongly converges with Egypt for the
1961-1990 and 1961-2000 periods (both X and Y are between 0 and 1), strongly diverges from
Iran for all four periods (with switching in 1961-1980 and 1961-1990), converges weakly
with Israel in 1961-1980 (X lies between 0 and 1 but Y is greater than unity), converges
strongly without switching with Morocco in all periods except 1961-1980 when convergence
is weak; converges strongly, without switching, with Syria in 1961-1990 and 1961-2000,
weakly in 1961-1980 and diverges strongly in 1961-1970; converges strongly, without
switching, with Tunisia in 1961-1980 and 1961-1990 but diverges strongly, without
switching, in 1961-1970 and with switching 1961-2000; and, finally, converges strongly,
without switching, with Turkey in 1961-1970, diverges strongly, with switching, in 19611980 and without switching, in 1961-1990 and 1961-2000.
6
Table 1
X and Y values: Base 1961
1961-1970
1961-1980
1961-1990
1961-2000
X
alg-egy alg-iran alg-isr alg-jor alg-mor
1.18
4.77
1.05 -18.62
0.87
1.43
-1.91
0.97 -6.99
0.96
0.90
-2.79
1.12 -15.57
0.70
0.33
2.30
1.38 -9.85
0.57
alg-syr alg-tun alg-tur
1.46
1.39
0.52
0.93
0.42
-1.07
0.93
0.03
1.42
0.36
-1.56
3.27
Y
alg-egy alg-iran alg-isr alg-jor alg-mor
1.14
5.71
1.09 -15.07
0.90
1.41
-1.81
1.03 -6.87
1.05
0.92
-2.36
1.19 -12.87
0.74
0.31
1.94
1.35 -6.94
0.50
alg-syr alg-tun alg-tur
1.33
1.35
0.51
1.01
0.48
-1.04
0.94
0.03
1.45
0.33
-1.63
2.94
1961-1970
1961-1980
1961-1990
1961-2000
egy-iran egy-isr egy-jor egy-mor egy-syr egy-tun egy-tur
1.74
1.10
0.25
-13.83
5.78
1.01
1.06
0.91
1.13
1.04
-21.22
-6.74
2.23
0.99
0.32
1.05
0.13
-9.06
1.31
1.59
0.99
0.64
1.02 -0.14
11.89
0.70
1.83
0.85
egy-iran egy-isr egy-jor egy-mor egy-syr egy-tun egy-tur
2.04
1.10
0.19
-13.82
4.98
0.93
1.00
0.77
1.11
0.92
-20.85
-6.69
2.33
0.86
0.27
1.14
0.11
-9.94
1.36
1.80
1.04
0.63
1.14 -0.12
12.30
0.77
2.24
0.89
1961-1970
1961-1980
1961-1990
1961-2000
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
0.65 13.14
1.47
1.95
2.40 -26.43
1.29 -0.09
0.52
0.50
-0.27
4.22
1.55
1.78
0.16
0.37
-0.81
28.14
1.28
6.65
0.84
0.65
-0.41
9.41
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
0.78 12.83
1.84
2.16
2.79 -30.87
1.23 -0.08
0.49
0.48
-0.27
3.60
1.43
1.24
0.14
0.32
-0.76 24.40
1.31
4.98
0.78
0.63
-0.45
8.92
1961-1970
1961-1980
1961-1990
1961-2000
1961-1970
1961-1980
1961-1990
1961-2000
isr-jor
1.57
1.18
1.57
1.68
isr-mor
0.99
0.97
0.97
1.10
isr-syr
1.20
0.96
1.05
1.01
isr-tun isr-tur
1.12
1.12
0.87
1.24
0.92
1.09
0.83
1.14
jor-mor
0.52
0.60
-0.05
0.09
jor-syr jor-tun jor-tur
1.10
0.57
2.67
0.58
-0.32
0.67
0.20
-1.54
6.43
-0.09
-2.39
7.13
isr-jor
1.36
1.16
1.43
1.49
isr-mor
1.05
1.04
1.10
1.17
isr-syr
1.14
1.03
1.14
1.13
isr-tun isr-tur
1.12
1.14
0.97
1.20
1.06
1.17
1.01
1.22
jor-mor
-0.02
0.59
-0.05
0.07
jor-syr jor-tun jor-tur
0.41
-0.47
4.87
0.57
-0.33
0.59
0.17
-1.40
5.46
-0.08
-2.22
5.70
1961-1970
1961-1980
1961-1990
1961-2000
mor-syr mor-tun mor-tur
15.00
0.47
0.81
0.07
1.38
0.61
6.19
1.20
0.82
-4.57
2.19
1.04
mor-syr mor-tun mor-tur
13.97
0.47
0.81
0.08
1.59
0.59
6.77
1.43
0.90
-4.75
2.56
1.04
1961-1970
1961-1980
1961-1990
1961-2000
syr-tun syr-tur
1.51
1.30
1.28
0.59
1.56
1.01
1.71
0.85
syr-tun syr-tur
1.31
1.15
1.50
0.58
1.76
1.05
2.11
0.89
1961-1970
1961-1980
1961-1990
1961-2000
tun-tur
1.11
-0.07
0.49
0.03
tun-tur
1.04
-0.07
0.55
0.03
7
Table 2
Numbers and Percentages of Strongly Diverging and
Converging Pairs
1961
1970
1980
1990
1961
1970
1980
1990
Strongly Diverging Pairs
1970
1980
1990
23 (63.9%) 14 (38.9%) 20 (55.6%)
13 (36.1%) 11 (30.6%)
20 (55.6%)
Strongly Converging Pairs
1970
1980
1990
6 (16.7%) 16 (44.4%) 13 (36.1%)
21 (58.3%) 20 (55.6%)
14 (38.9%)
2000
21 (58.3%)
14 (38.9%)
18 (50.0%)
19 (52.8%)
2000
14 (38.9%)
21 (58.3%)
11 (30.6%)
17 (47.2%)
An overall picture of convergence may be obtained from Table 2 where the numbers
and percentages of strongly diverging and converging pairs are given for each period. We
note that, for the 1961 based calculations, the number of strongly diverging pairs are higher
than the number of strongly converging pairs except in 1961-1980. It is difficult to see a
distinct pattern here except that the number of strongly diverging pairs is much higher than
the number of strongly converging pairs in 1961-1970 but this difference diminishes in later
periods. On the other hand, we find a reverse picture when 1970 is taken as the base; the
number of converging pairs is higher than the number of diverging pairs in all three periods.
This picture, however, does not continue for the 1980 and 1990 based calculations; the
number of strongly divergent pairs is dominant in these cases.
The overall picture that we obtain from Table 2 does not lead us to a clear cut
conclusion as to whether convergence or divergence is the dominant trend for the nine
countries that we have considered for the MENA region. We shall take this a step further and
first choose those pairs that this analysis suggests to be exhibiting strong convergence
behaviour and then subject them to unit root tests so that statistically stronger results may be
obtained.
The choice of the pairs in question was first made by tabulating, for each country, the
countries with which strong convergence evidence was found. These are given in Table 3 and
8
in Tables A4 to A7 in the Appendix. For each country we counted the number of times it was
paired with another country in its
Table 3
Strongly Converging Pairs for Algeria and Egypt
ALGERIA
Without Switching
EGYPT
Without Switching
Base Year
1961
1970
Base Year
1970
Morocco
Turkey
1980
Tunisia
Israel
Jordan
Syria
Tunisia
1980
1990
1990
2000
Egypt
Egypt
Morocco Morocco
Syria
Syria
Tunisia
Egypt
Egypt
Jordan
Iran
Morocco
Jordan
Syria Morocco
Tunisia
Syria
Egypt
Egypt
Morocco Morocco
Tunisia
Syria
Egypt
Jordan
Morocco
Syria
1961
1970
1980
1970
Jordan
1980
Iran
Turkey
1990
Algeria
Iran
Jordan
Iran
Turkey
Algeria
Iran
Jordan
Morocco
Syria
Algeria
Iran
Jordan
Morocco
Tunisia
1990
Iran
Iran
1961
1970
Iran
1980
Algeria
Iran
Tunisia
Algeria
Syria
Israel
Turkey
With Switching
1961
1970
1980
1990
2000
Algeria
Iran
Syria
Turkey
Algeria
Iran
Syria
Turkey
With Switching
Jordan
Jordan
Jordan
Morocco
Jordan
Morocco
1990
Table and chose those pairs that occurred four or more times. For example, if we again
consider Algeria, as given in Table 3, we find that it has been paired with Morocco 8 times,
with Egypt and Syria 7 times with Tunisia 5 times and with Jordan and Iran 4 times. Hence,
the pairs we shall consider from this Table are Algeria-Morocco, Algeria-Egypt, AlgeriaSyria, Algeria -Tunisia, Algeria-Jordan and Algeria-Iran.
In Table 3 we also have Egypt and we find that it is paired with Jordan and Iran 8
times, with Algeria 7 times, with Syria 6 times, with Turkey 5 times and with Morocco 4
times. The additional pairs we shall consider from Table 3 then become Egypt-Jordan, Egypt-
9
Iran, Egypt-Syria, Egypt-Turkey, and Egypt-Morocco. Egypt-Algeria has, of course, been left
out to avoid double-counting. Proceeding this way we find that Table A4 yields the pairs IranMorocco, Iran-Tunisia, Iran-Syria, Iran-Algeria, Iran-Jordan, Israel-Syria and Israel-Tunisia;
Table A5, the pairs Jordan-Morocco, Jordan-Syria, Morocco-Syria and Morocco-Turkey;
Table A6, the pairs Syria-Turkey and Tunisia-Turkey. Since all countries that pair with
Turkey have been accounted for we obtain no additional pairs from Table A7.
Table 4
ADF Test Results
Intercept
Intercept and Trend
p
ADF
p
ADF
Algeria-Egypt
Algeria-Morocco
Algeria-Syria
Algeria-Tunisia
Algeria-Jordan
Algeria-Iran
Egypt-Iran
Egypt-Turkey
Egypt-Jordan
Egypt-Syria
Egypt-Morocco
Iran-Morocco
Iran-Syria
Iran-Tunisia
Iran-Jordan
Israel-Syria
Israel-Tunisia
Jordan-Morocco
Jordan-Syria
Morocco-Turkey
Morocco-Syria
Syria-Turkey
Tunisia-Turkey
0
9
0
8
3
3
0
1
0
0
0
3
0
0
3
8
1
3
0
1
0
0
0
-0.5662 (0.8666)
-2.6781 (0.0896)*
-2.7006 (0.0830)*
2.0903 (0.9998)
-2.1913 (0.2127)
-1.5842 (0.4801)
-0.7893 (0.8110)
-1.8465 (0.3531)
-0.7962 (0.8091)
-3.0141 (0.0423)**
-1.2095 (0.6607)
-1.5387 (0.5029)
-1.4863 (0.5299)
-1.7194 (0.8300)
-2.5185 (0.1196)
-3.4311 (0.0174)**
-1.2688 (0.6340)
-2.3111 (0.1741)
-2.2700 (0.1864)
-2.0281 (0.2741)
-3.0688 (0.0374)**
-3.2492 (0.0245)**
-0.9835 (0.7497)
1
1
0
9
3
3
3
3
7
0
0
0
0
8
3
8
9
3
8
1
0
0
0
-1.9470 (0.6105)
-2.3424 (0.4022)
-3.2068 (0.0980)*
-0.5220 (0.9768)
-2.1218 (0.5168)
-1.8162 (0.6759)
-2.9673 (0.1550)
-3.0654 (0.1297)
-2.5131 (0.3201)
-3.0955 (0.1215)
-2.5441 (0.3066)
-1.1657 (0.9037)
-1.9524 (0.6082)
-2.3361 (0.4035)
-2.7349 (0.2312)
-3.8312 (0.0281)**
-3.1175 (0.1206)
-2.4125 (0.3673)
-2.2458 (0.4493)
-2.5181 (0.3182)
-3.4067 (0.0651)**
-3.2350 (0.0926)*
-1.8505 (0.6606)
Notes: 1. The figures in parentheses are p-values. They are based on
MacKinnon (1996). 2. * Significant at the 10% level, ** Significant at the 5%
level
The ADF test results for those chosen pairs are given in Table 4. When there is both an
intercept and a trend term in (5); i.e., when r =1, we find that the per capita incomes of
Algeria and Syria, Israel and Syria, Morocco and Syria, and Syria and Turkey converge. The
tests of the trend term for these pairs are given in Table 5 from which we note that the trend
term is not significant for any of these pairs. This, of course, implies that these pairs do not
contain a common deterministic trend term. We then turn to the results for the model with
10
Table 5
Testing the Significance of the Trend Term
in Models with Intercept and Trend where
the Unit Root Hypothesis has been Rejected
Trend
Algeria-Syria
-0.0033
(-1.6629)
(0.1050)
Israel-Syria
-0.0028
(-1.4907)
(0.1517)
Morocco-Syria
-0.0023
(-1.4410)
(0.1582)
Syria-Turkey
-0.0007
(-0.4156)
(0.6801)
Notes: The first parenthesis under the coefficient
estimates is the t-ratio while the second is its pvalue based on the standard normal distribution.
only an intercept term (i.e., r = 0) and find that the same four pairs also converge in this case.
In addition, we also find that the pairs Algeria-Morocco and Egypt-Syria also converge. The
evidence, in the case of Algeria-Morocco, is not very strong, however, the significance level
being only 10%.
Turning to the KPSS results in Table 6, we now find the number of converging pairs
to be 11. Pesaran (2006) provides similar figures based on testing for all 36 pairs. Evidence
regarding the four converging pairs based on the ADF test is also obtained in this case if we
regard the 10% percent significance of the KPSS statistic for Algeria-Syria as indicating
convergence because it is below the 5% level. However, in addition to these four pairs, we
have Algeria-Morocco (that also converged in the ADF case), Algeria-Jordan, Algeria-Iran,
Egypt-Turkey, Egypt-Syria (that also converged in the ADF case), Iran-Jordan, JordanMorocco and Morocco-Turkey.
However, when we plot the zijt’s for some of the nonconverging pairs, as given in
Figure 1, we note that they show structural shifts in their levels. This is quite clear, for
example, in the case of Algeria-Egypt, Egypt-Iran and Egypt-Syria. Thus, we applied the
sequential unit root testing procedure described in Section 2, which involved sequentially
estimating equation (9). The results are given in Table 7.
11
Figure 1
Plots of Selected Pairs
Algeria_Egypt
Algeria_Iran
.8
Algeria_Jordan
.4
Algeria_Tunisia
.6
.6
.7
.2
.5
.0
.4
-.2
.4
.4
.6
.2
.2
.0
.3
.0
-.4
-.2
.2
.1
-.6
65
70
75
80
85
90
95
00
-.2
65
70
Egypt_Iran
75
80
85
90
95
00
-.4
65
70
Egypt_Jordan
0.0
-0.2
80
85
90
95
00
65
70
Iran_Jordan
.1
1.0
.0
0.8
-.1
-0.4
75
75
80
85
90
95
00
90
95
00
Iran_Morocco
1.0
0.8
0.6
0.6
-.2
-0.6
0.4
-.3
-0.8
0.4
0.2
-.4
-1.0
-.5
0.0
-1.2
-.6
-0.2
65
70
75
80
85
90
95
00
65
70
Iran_Syria
75
80
85
90
95
00
0.2
0.0
65
70
Iran_Tunisia
1.2
.8
1.0
.6
0.8
.4
0.6
.2
0.4
.0
0.2
-.2
75
80
85
90
95
00
90
95
00
Iran_Turkey
.6
.4
.2
.0
0.0
-.2
-.4
65
70
75
80
85
90
95
00
-.4
65
70
75
80
85
90
95
00
12
65
70
75
80
85
65
70
75
80
85
Table 6
KPSS Test Results
m
KPSS
Algeria-Egypt
5
0.3637*
Algeria-Morocco
4
0.2543
Algeria-Syria
4
0.3752*
Algeria-Tunisia
5
0.6020**
Algeria-Jordan
4
0.1593
Algeria-Iran
5
0.2921
Egypt-Iran
5
0.4772**
Egypt-Turkey
4
0.3160
Egypt-Jordan
5
0.3776*
Egypt-Syria
4
0.1499
Egypt-Morocco
5
0.3873*
Iran-Morocco
5
0.4201*
Iran-Syria
5
0.4372*
Iran-Tunisia
5
0.6077**
Iran-Jordan
5
0.1657
Israel-Syria
4
0.0742
Israel-Tunisia
5
0.5458**
Jordan-Morocco
5
0.1881
Jordan-Syria
4
0.4755**
Morocco-Turkey
4
0.2499
Morocco-Syria
4
0.2430
Syria-Turkey
4
0.1282
Tunisia-Turkey
5
0.5771**
Notes: 1. The critical values for the KPSS test are
from Table 1 of Kwiatowski et al (1992):
10%
0.347
5%
0.463
2. * Significant at the 10% level,
5% level+
1%
0.739
**
Significant at the
.
We note, in the intercept and trend case, that there are five converging pairs; AlgeriaEgypt, Egypt-Morocco, Iran-Syria, Israel-Syria, Morocco-Turkey and Syria-Turkey. Only
two of these are the same pairs that had converged according to the ADF results of Table 4.
When we test if the trend terms for these pairs are significant, we find, from Table 8, that only
for Iran-Syria and Israel-Syria is it not significant. For the other five pairs, we have to
conclude that convergence takes place in the presence of a common deterministic trend. We
also note that the structural shifts, as represented by the estimates associated with the dummy
variables, are all significant.
When we turn to the results of the intercept case, we find that there are only three pairs
converging; Iran-Syria, Morocco-Syria and Syria-Turkey. We already have evidence on the
convergence of Syria-Turkey from the ADF results. One can, probably, also claim
13
convergence for Israel-Syria as the value of min ADF is extremely close to the critical value
at the 10% level.
Table 7
Min ADF Test Results
Intercept
Intercept and Trend
p min ADF
p
min ADF
ĥ
ĥ
Algeria-Egypt
Algeria-Morocco
Algeria-Syria
Algeria-Tunisia
Algeria-Jordan
Algeria-Iran
Egypt-Iran
Egypt-Turkey
Egypt-Jordan
Egypt-Syria
Egypt-Morocco
Iran-Morocco
Iran-Syria
Iran-Tunisia
Iran-Jordan
Israel-Syria
Israel-Tunisia
Jordan-Morocco
Jordan-Syria
Morocco-Turkey
Morocco-Syria
Syria-Turkey
Tunisia-Turkey
1
1
3
5
3
3
5
1
5
1
1
3
3
3
3
5
0
3
1
1
5
5
0
-3.7601
-3.8300
-3.1968
-3.8245
-2.3463
-2.9582
-4.1202
-2.7619
-2.5360
-2.5802
-2.1767
-3.6217
-5.4829***
-4.0439
-3.3946
-4.1847
-3.8898
-2.9261
-2.9595
-3.0051
-4.5957**
-4.8638**
-3.1454
1989
1987
1990
1987
1977
1976
1979
1978
1988
1982
1989
1978
1979
1978
1977
1977
1974
1987
1987
1990
1977
1977
1970
1
1
3
4
3
3
5
3
5
4
4
3
4
3
3
3
1
3
3
0
5
5
1
-5.4318***
-4.7269
-3.2256
-3.1696
-2.5987
-3.7269
-3.8822
-4.8321**
-3.5617
-3.8982
-5.3762***
-3.5664
-5.7118***
-4.2788
-4.1079
-4.5963*
-3.6736
-3.6221
-3.9672
-7.4049***
-4.4968
-5.6185***
-3.5463
1971
1987
1990
1978
1977
1978
1979
1973
1977
1973
1973
1978
1979
1978
1977
1977
1974
1977
1975
1978
1977
1979
1986
Notes: 1. The asymptotic critical values for the min ADF test in the case of only
an intercept have been obtained from Perron and Vogelsang (1992), Table 2 and
are given as
0.10
-4.19
0.05
-4.44
0.025
-4.69
0.01
-4.95
2. The asymptotic critical values for the min ADF test in the case of an intercept
and a trend term have been obtained from Perron (1997), Table 1 and are given as
0.10
-4.58
0.05
-4.80
3. * Significant at the 10% level,
the 1% level
**
0.025
-5.02
0.01
-5.41
Significant at the 5% level,
**
Significant at
In sum, of these test results the most favourable ones are those obtained from the
KPPS tests. An exercise as to whether convergence clubs may be obtained from these results
seems to indicate the following groupings: Algeria-Morocco-Syria, Algeria-Jordan-Iran,
Syria-Egypt-Turkey. These groups overlap, so it is difficult to call them convergence clubs.
14
Table 8
Testing the Significance of the Trend Term in Models with
Intercept and Trend with Shift in the Intercept and where
the Unit Root Hypothesis has been Rejected
Trend
DU( ĥ )
D( ĥ )
Algeria-Egypt
-0.0103
0.1515
-0.2616
(-7.2750)
(4.7608)
(-5.5676)
(0.0000)*** (0.0000)***
(0.0000)***
Egypt-Morocco
0.0141
-0.2430
0.1453
(5.7236)
(-4.9533)
(2.6540)
(0.0000)*** (0.0000)***
(0.0134)**
Egypt-Turkey
0.0079
-0.1455
0.0798
(4.0838)
(-3.3557)
(1.4236)
(0.0003)*** (0.0023)***
(0.1656)
Iran-Syria
0.0037
-0.5722
0.3676
(1.0818)
(-4.9849)
(2.5645)
(0.2893)
(0.0000)***
(0.0165)**
Israel-Syria
0.0039
-0.1066
0.3850
(1.6971)
(-2.0087)
(4.5808)
(0.1008)
(0.0543)*
(0.0001)***
Morocco-Turkey
-0.0089
0.1789
-0.0976
(-5.7679)
(5.1377)
(-1.9907)
(0.0000)*** (0.0000)***
(0.0546)*
Syria-Turkey
-0.0110
0.3927
-0.2562
(-3.5254)
(4.6281)
(-2.1493)
(0.0017)*** (0.0001)***
(0.0419)**
Notes: 1. The first parenthesis under the coefficient estimates is the t-ratio
while the second is its p-value based on the standard normal distribution.
2. * Significant at the 10% level, ** Significant at the 5% level, **
Significant at the 1% level
The converging pairs based on the other tests are so few in number that such an exercise does
not seem possible.
5. Conclusions
In investigating the per capita income convergence of the MENA countires, we used a
pair-wise testing approach as opposed to the panel unit root approach implemented by Guetat
and Serranita (2004), where the convergence of countries to a target variable was sought after.
We first subjected the nine countries, for which a complete data set was available, to a
descriptive procedure due to Webber and White (2004) and then applied unit root tests that
both excluded and included structural shifts in the levels of the variables in question. Our
conclusions are as follows:
15
1. The descriptive procedure yielded results that differed depending upon the base
year and the length of the period for which comparisons of per capita income
between two countries were made. When 1961, 1980 and 1990 were chosen as the
base year, the number of converging pairs was usually less than the diverging ones
but this number appeard to increase as the period became longer. For 1970 as the
base year, however, the number of converging pairs exceeded the number of
diverging pairs.
2. We chose 23 pairs that we subjected to unit root tests. The ADF results yielded
four converging pairs while the KPSS results gave us eleven such pairs. When we
took the possibility of shifts in the intercept term into account, we obtained seven
converging pairs but, as opposed to the previous ADF results, five of these pairs
appeared to have common deterministic trends.
3. An exercise to see if we may identify convergence clubs based on the KPSS results
was not fruitful.
4. Hence, we may state that convergence among the nine countries under
consideration is not a dominant phenomenon. Whether, as Guetat and Serranito
(2004) seem to have found, different groupings of these countries based on
exogeneous criteria may lead us to revise this conclusion is a point we intend to
look into.
References
Bernard, A.B. and S. Durlauf (1995): “Convergence in International Output”, Journal of
Applied Econometrics, 10, 97-102.
Guetat, I. And F. Serranito (2004): “Using Panel Unit Root Tests to Evaluate the Income
Convergence Hypothesis in Middle East and North African Countries”, Cahiers de la
Maison de Sciences Economiques, Serie Blanche, TEAM-CNRS, Paris I.
Heston, A., R. Summers and B. Aten (2002): “Penn World Table Version 6.1:, Center for
International Comparisons at the University of Pennsylvania (CICUP).
Kwiatowski, D., P.C.B. Phillips, P. Schmidt and Y. Shin (1992): “Testing the Null Hypothesis
of Stationarity Against the Alternative of a Unit Root”, Journal of Econometrics, 54,
159-178.
MacKinnon, J.G. (1996): “Numerical Distribution Functions for Unit Root and Cointegration
Tests”, Journal of Applied Econometrics, 11, 601-618.
16
Newey, W. And K. West (1994): “Automatic Lag Selection in Covariance Matrix
Estimation”, Review of Economic Studies, 61, 631-653.
Perron, P. (1996): “Further Evidence on Breaking Trend Functions in Macroeconomic
Variables”, Journal of Econometrics, 80, 355-385.
Perron. P. and T.J. Vogelsang (1992): “Nonstationarity and Level Shifts with an Application
to Purchasing Power Parity”, Journal of Business and Economic Statistics, 10(3), 301320.
Pesaran, M.H. (2006): “A Pair-Wise Approach to Testing Output and Growth Convergence`,
forthcoming in the Journal of Econometrics.
Webber, D.T. and P. White (2004): “Concordant Convergence Empirics`, Discussion Paper,
School of Economics, University of the West of England.
17
Table A1
X and Y values: Base 1970
1970-1980
1970-1990
1970-2000
X
alg-egy alg-iran alg-isr alg-jor alg-mor
1.22
-0.40
0.92
0.38
1.11
0.77
-0.59
1.07
0.84
0.80
0.28
0.48
1.31
0.53
0.66
alg-syr alg-tun alg-tur
0.63
0.30
-2.08
0.63
0.02
2.76
0.24
-1.12
6.34
1970-1980
1970-1990
1970-2000
egy-iran egy-isr egy-jor egy-mor egy-syr egy-tun egy-tur
0.52
1.03
4.16
1.53
-1.17
2.21
0.93
0.18
0.96
0.52
0.65
0.23
1.58
0.94
0.37
0.93
-0.58
-0.86
0.12
1.82
0.81
1970-1980
1970-1990
1970-2000
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
1.98
-0.01
0.35
0.26
-0.11
-0.16
2.39
0.14
0.11
0.19
-0.34
-1.06
1.98
0.51
0.57
0.33
-0.17
-0.36
1970-1980
1970-1990
1970-2000
1970-1980
1970-1990
1970-2000
isr-jor
0.75
1.00
1.07
isr-mor
0.98
0.99
1.11
isr-syr
0.80
0.88
0.85
isr-tun isr-tur
0.78
1.10
0.82
0.97
0.74
1.02
jor-mor
-21.04
1.81
-3.26
jor-syr jor-tun jor-tur
1.00
0.52
0.11
0.35
2.50
1.04
-0.16
3.90
1.16
1970-1980
1970-1990
1970-2000
mor-syr mor-tun mor-tur
0.00
2.95
0.76
0.41
2.58
1.02
-0.30
4.70
1.29
1970-1980
1970-1990
1970-2000
syr-tun syr-tur
0.85
0.45
1.03
0.78
1.13
0.65
1970-1980
1970-1990
1970-2000
tun-tur
-0.06
0.44
0.02
18
Y
alg-egy alg-iran alg-isr alg-jor alg-mor
1.23
-0.32
0.95
0.46
1.16
0.80
-0.41
1.10
0.85
0.82
0.27
0.34
1.24
0.46
0.56
alg-syr
0.76
0.71
0.25
alg-tun
0.36
0.02
-1.21
alg-tur
-2.05
2.86
5.79
egy-iran egy-isr egy-jor egy-mor egy-syr
0.38
1.01
4.84
1.51
-1.34
0.13
1.03
0.57
0.72
0.27
0.31
1.03
-0.62
-0.89
0.15
egy-tun
2.49
1.93
2.40
egy-tur
0.86
1.03
0.89
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
1.58
-0.01
0.27
0.22
-0.10
-0.12
1.84
0.10
0.08
0.15
-0.27
-0.79
1.68
0.39
0.43
0.29
-0.16
-0.29
isr-jor
0.86
1.05
1.10
isr-mor
0.99
1.05
1.12
isr-syr
0.90
1.00
0.99
isr-tun
0.87
0.95
0.90
isr-tur
1.05
1.03
1.08
jor-mor
-25.22
1.93
-3.06
jor-syr
1.40
0.40
-0.19
jor-tun
0.71
2.97
4.70
jor-tur
0.12
1.12
1.17
mor-syr mor-tun mor-tur
0.00
0.83
0.77
0.48
3.08
1.10
-0.34
5.51
1.27
syr-tun
1.15
1.35
1.61
syr-tur
0.50
0.91
0.77
tun-tur
-0.07
0.52
0.03
Table A2
X and Y values: Base 1980
1980-1990
1980-2000
alg-egy
0.63
0.23
X
alg-iran alg-isr alg-jor alg-mor
1.47
1.15
2.23
0.72
-1.21
1.42
1.41
0.59
alg-syr alg-tun alg-tur
1.00
0.06
-1.33
0.38
-3.69
-3.05
1980-1990
1980-2000
egy-iran egy-isr egy-jor egy-mor egy-syr egy-tun egy-tur
0.35
0.93
0.12
0.43
-0.19
0.71
1.01
0.71
0.90
-0.14
-0.56
-0.10
0.82
0.87
1980-1990
1980-2000
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
1.20 -20.32
0.30
0.74
3.01
6.67
1.00 -76.03
1.61
1.28
1.53
2.23
1980-1990
1980-2000
1980-1990
1980-2000
isr-jor
1.32
1.42
isr-mor
1.00
1.13
isr-syr
1.10
1.06
isr-tun isr-tur
1.05
0.88
0.95
0.92
jor-mor
-0.09
0.15
jor-syr jor-tun jor-tur
0.35
4.79
9.56
-0.16
7.46
10.61
1980-1990
1980-2000
mor-syr mor-tun mor-tur
88.72
0.88
1.35
-65.43
1.59
1.71
1980-1990
1980-2000
syr-tun syr-tur
1.22
1.71
1.33
1.44
1980-1990
1980-2000
tun-tur
-7.08
-0.39
19
Y
alg-egy alg-iran alg-isr alg-jor alg-mor
0.65
1.31
1.15
1.87
0.71
0.22
-1.07
1.30
1.01
0.48
alg-syr
0.93
0.33
alg-tun
0.06
-3.37
alg-tur
-1.39
-2.83
egy-iran egy-isr egy-jor egy-mor egy-syr
0.35
1.02
0.12
0.48
-0.20
0.81
1.02
-0.13
-0.59
-0.11
egy-tun
0.78
0.96
egy-tur
1.20
1.03
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
1.17 -16.37
0.28
0.66
2.80
6.79
1.07 -66.02
1.59
1.32
1.68
2.48
isr-jor
1.22
1.28
isr-mor
1.06
1.13
isr-syr
1.11
1.10
isr-tun
1.09
1.04
isr-tur
0.98
1.02
jor-mor
-0.08
0.12
jor-syr
0.29
-0.14
jor-tun
4.20
6.65
jor-tur
9.19
9.61
mor-syr mor-tun mor-tur
87.64
0.90
1.52
-61.49
1.61
1.76
syr-tun
1.18
1.41
syr-tur
1.82
1.54
tun-tur
-7.76
-0.44
Table A3
X and Y values: Base 1990
1990-2000
X
alg-egy alg-iran alg-isr alg-jor alg-mor
0.37
-0.82
1.23
0.63
0.82
alg-syr alg-tun alg-tur
0.38 -57.18
2.30
1990-2000
egy-iran egy-isr egy-jor egy-mor egy-syr egy-tun egy-tur
2.00
0.97
-1.12
-1.31
0.53
1.15
0.86
1990-2000
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
0.83
3.74
5.36
1.73
0.51
0.33
1990-2000
1990-2000
isr-jor
1.07
isr-mor
1.13
isr-syr
0.96
isr-tun isr-tur
0.90
1.05
jor-mor
-1.80
jor-syr
-0.47
jor-tun jor-tur
1.56
1.11
1990-2000
mor-syr mor-tun mor-tur
-0.74
1.82
1.27
1990-2000
syr-tun syr-tur
1.09
0.84
1990-2000
tun-tur
0.05
20
Y
alg-egy alg-iran alg-isr alg-jor alg-mor
0.34
-0.82
1.13
0.54
0.68
alg-syr
0.35
alg-tun
-54.21
alg-tur
2.03
egy-iran egy-isr egy-jor egy-mor egy-syr
2.30
1.00
-1.09
-1.24
0.56
egy-tun
1.24
egy-tur
0.86
iran-isr iran-jor iran-mor iran-syr iran-tun iran-tur
0.91
4.03
5.58
2.01
0.60
0.37
isr-jor
1.04
isr-mor
1.07
isr-syr
0.99
isr-tun
0.95
isr-tur
1.04
jor-mor
-1.58
jor-syr
-0.47
jor-tun
1.58
jor-tur
1.04
mor-syr mor-tun mor-tur
-0.70
1.79
1.15
syr-tun
1.19
syr-tur
0.85
tun-tur
0.06
Table A4
Strongly Converging Pairs for Iran and Israel
IRAN
Without Switching
ISRAEL
Without Switching
Base Year
1961
Base Year
1970
Israel
1970
1980
Egypt
Morocco
Syria
Egypt
Morocco
Syria
1980
1990
Egypt
Morocco
Syria
Egypt
Jordan
Morocco
Syria
Egypt
Morocco
Syria
1990
1961
1970
2000
Egypt
Morocco
Syria
Algeria
Egypt
Jordan
Morocco
Syria
Egypt
1961
1970
1980
1990
1980
1990
2000
Algeria
Jordan
Morocco
Syria
Tunisia
Syria
Tunisia
Syria
Tunisia
1980
1990
Tunisia
Israel
Turkey
With Switching
Jordan
Tunisia
Tunisia
Algeria
Algeria
Jordan
Tunisia
Tunisia
Turkey
1970
Iran
Morocco
Turkey
Egypt
Iran
Syria
Tunisia
With Switching
1961
1970
1980
1990
Tunisia
Tunisia
Turkey
Algeria
Table A5
Strongly Converging Pairs for Jordan and Morocco
JORDAN
Without Switching
MOROCCO
Without Switching
Base Year
1961
1970
1980
Base Year
1970
Egypt
1980
Morocco
Syria
Turkey
Algeria
Israel
Tunisia
Turkey
1990
Egypt
Syria
2000
Morocco
Algeria
Egypt
Iran
Syria
Egypt
Syria
Algeria
Iran
Jordan
Morocco
Morocco
1990
1961
1970
1980
1990
1961
1970
1970
Algeria
Israel
Tunisia
Turkey
1980
Iran
Jordan
Syria
Turkey
Iran
Israel
Turkey
1980
Algeria
With Switching
Egypt Morocco
Iran
Tunisia
Iran
Morocco
Egypt
Syria
1990
Algeria
Iran
Turkey
2000
Algeria
Iran
Jordan
Algeria
Egypt
Iran
Syria
Algeria
Egypt
Iran
Tunisia
Algeria
Iran
1990
Algeria
Iran
Algeria
With Switching
Egypt
Syria
Egypt
Syria
Syria
1961
1970
1980
1990
21
Jordan
Egypt
Syria
Jordan
Egypt
Syria
Table A6
Strongly Converging Pairs for Syria and Tunisia
SYRIA
Without Switching
TUNISIA
Without Switching
Base Year
Base Year
1970
1961
1970
1980
Jordan
Morocco
Turkey
1990
Algeria
Jordan
Iran
Algeria
Iran
Israel
Turkey
Algeria
Egypt
Iran
Israel
Jordan
Morocco
Turkey
Iran
Jordan
1980
1990
2000
Algeria
Egypt
Iran
Turkey
Algeria
Egypt
Iran
Israel
Turkey
1961
1970
1980
Algeria
1961
1970
1980
1990
With Switching
1980
1990
Egypt
1980
Algeria
Israel
Algeria
Israel
Jordan
1990
Algeria
Turkey
Algeria
Israel
Turkey
Algeria
Egypt
Morocco
1990
Algeria
Egypt
Israel
Turkey
1961
1970
1970
Morocco
Jordan
Jordan
Morocco
Egypt
Jordan
Jordan
Morocco
22
2000
Turkey
Israel
Turkey
Egypt
Iran
Iran
Israel
Turkey
With Switching
Jordan
Turkey
Iran
Turkey
Iran
Iran
Iran
Iran
Turkey
Table A7
Strongly Converging Pairs for Turkey
TURKEY
Without Switching
Base Year
2000
1990
1980
1970
Egypt
Egypt Morocco
Morocco
1961
Syria
Tunisia
Jordan
Tunisia
Morocco
Syria
Egypt
Syria
Egypt
1970
Syria
Tunisia
Jordan
Tunisia
Morocco
Syria
Israel
1980
Egypt
1990
Iran
Syria
Tunisia
With Switching
Tunisia
1961
Iran
Iran
1970
Tunisia
Tunisia
1980
1990
23